Non-invasive visualization of flow dynamics in human arteries is widely considered to be of high diagnostic importance as it may foster clinical detection of abnormal vascular conditions (Steinman D A, Taylor C A. Flow imaging and computing: large artery hemodynamics. Ann. Biomed. Eng., 2005; 33: 1704-1709). For instance, monitoring flow patterns in the carotid arteries has long been implicated in useful in stroke prognosis (Donnan G A, Fisher M, Macleod M, Davis S M. Stroke. Lancet, 2008; 371: 1612-1623; Shields R C. Medical management of carotid stenosis. Perspect. Vasc. Surg. Endovasc. Ther., 2010; 22: 18-27). Over the years, a few non-invasive flow imaging modalities have been developed (Owen A R, Roditi G H. Peripheral arterial disease: the evolving role of non-invasive imaging. Postgrad. Med. J., 2011; 87: 189-198; Wolbarst A B, Hendee W R. Evolving and experimental technologies in medical imaging. Radiology, 2006; 238: 16-39), and among them, ultrasound has perhaps established itself as a unique bedside modality that can be readily applied to point-of-care diagnoses (Bierig S M, Jones A. Accuracy and cost comparison of ultrasound versus alternative imaging modalities, including CT, MR, PET, and angiography. J. Diagnost. Med. Sonography, 2009; 25: 138-144; Moore C L, Copel J A. Point-of-care ultrasonography. New Eng. J. Med., 2011; 364: 749-757). In most existing ultrasound scanners, flow information can be rendered in real-time in the form of color flow images, which provide 2-D maps of axial flow velocity (or flow power) over an imaging view (Evans D H. Color flow and motion imaging. Proc. Inst. Mech. Eng. H, 2010; 224: 241-253; Hoskins P R, McDicken W N. Colour ultrasound imaging of blood flow and tissue motion. Br. J. Radiol., 1997; 70: 878-890). This flow imaging mode, when used together with the Doppler spectrogram mode that plots the temporal flow profile at a single range gate, can offer vast information about flow behavior in both spatial and temporal dimensions (Gaitini D, Soudack M. Diagnosing carotid stenosis by Doppler sonography: state of the art. J. Ultrasound Med., 2005; 24: 1127-1136; Hoskins P R. Haemodynamics and blood flow measured using ultrasound imaging. Proc. Inst. Mech. Eng. H, 2010; 224: 255-271).
Despite its popular role in clinical screening, ultrasound color flow imaging is known to possess method flaws (Evans 2010). In particular, as its operating principle is typically based on axial Doppler estimation, it is prone to error if the beam-flow angle (i.e. angle between the ultrasound propagation axis and the flow trajectory) varies over the vasculature (Evans D H, Jensen J A, Nielsen M B. Ultrasound color Doppler imaging. Interface Focus, 2011; 1: 490-502). This issue represents a significant pitfall in diagnostic scenarios where the vasculature is not in straight-tube form, such as the bifurcation geometry found in the carotid arteries (Ku D N. Blood flow in arteries. Annu. Rev. Fluid Mech., 1997; 29: 399-434). In these cases, it can be challenging for sonographers to properly interpret color flow images (Arning C, Eckert B. The diagnostic relevance of colour Doppler artefacts in carotid artery examinations. Eur. J. Radiol., 2004; 51: 246-251; Rubens D J, Bhatt S, Nedelka S, Cullinan J. Doppler artifacts and pitfalls. Radiol. Clin. N. Am., 2006; 44: 805-835), especially when exacerbated by pulsatile flow conditions with considerable temporal variations in flow velocities.
For ultrasound to succeed in providing unambiguous mapping of flow dynamics in tortuous vasculature, it is imperative to resolve the beam-flow angle dependence problem and in turn derive velocity estimates that reflect the actual flow characteristics (Dunmire B, Beach K W, Labs K H, Plett M, Strandness Jr D E. Cross-beam vector Doppler ultrasound for angle-independent velocity measurements, Ultrasound Med. Biol., 2000, 26: 1213-1235; Tortoli P, Bambi G, Ricci S. Accurate Doppler angle estimation for vector flow measurements. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2006; 53: 1425-1431; Tortoli P, Dallai A, Boni E, Francalanci L, Ricci S., “An automatic angle tracking procedure for feasible vector Doppler blood velocity measurements,” Ultrasound Med. Biol. (2010), 36: 488-496). To fulfill this task, flow estimation needs to be performed not only along the axial direction (as is the case in color flow imaging) but also the lateral direction of the imaging view, so that both the flow angle and the velocity magnitude can be determined without uncertainty (Evans et al. 2011). Motivated by such rationale, new imaging paradigms for flow vector estimation have been proposed. Often categorized as vector flow imaging methods, these paradigms are generally based on four types of estimation principles: (i) multi-angle Doppler analysis (Capineri L, Scabia M, Masotti L. A Doppler system for dynamic vector velocity maps. Ultrasound Med. Biol., 2002; 28: 237-248; Kripfgans O D, Rubin J M, Hall A L, Fowlkes J B. Vector Doppler imaging of a spinning disc ultrasound Doppler phantom. Ultrasound Med. Biol., 2006; 32: 1037-1046; Pastorelli A, Torricelli G, Scabia M, Biagi E, Masotti L. A real-time 2-D vector Doppler system for clinical experimentation. IEEE Trans. Med. Imag., 2008; 27: 1515-1524; (ii) biaxial phase shift estimation from acoustic fields with transverse oscillations (Pedersen M M, Pihl M J, Haugaard P, Hansen J M, Hansen K L, Nielsen M B, Jensen J A. Comparison of real-time in vivo spectral and vector velocity estimation. Ultrasound Med. Biol., 2012; 39: 145-151; Udesen J, Jensen J A. Investigation of transverse oscillation method. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2006; 53: 959-971; Udesen J, Nielsen M B, Nielsen K R, Jensen J A. Examples of in vivo blood vector velocity estimation. Ultrasound Med. Biol., 2007; 33: 541-548); (iii) inter-frame blood speckle tracking (Bohs L N, Geiman B J, Anderson M E, Gebhart S C, Trahey G E. Speckle tracking for multi-dimensional flow estimation. Ultrasonics, 2000; 38: 369-375; Ebbini E S. Phase-coupled two-dimensional speckle tracking algorithm. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2006; 53: 972-990; Xu T, Bashford G R. Two-dimensional blood flow velocity estimation using ultrasound speckle pattern dependence on scan direction and A-line acquisition velocity. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2013; 60: 898-908); and (iv) directional cross-correlation analysis (Jensen J A. Directional velocity estimation using focusing along the flow direction I: theory and simulation. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2003; 50: 857-872; Jensen J A, Bjerngaard R. Directional velocity estimation using focusing along the flow direction II: experimental investigation. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2003; 50: 873-880; Kortbek J, Jensen J A. Estimation of velocity vector angles using the directional cross-correlation method. IEEE Trans. Ultrason. Ferroelec Freq. Contr., 2006; 53: 2036-2049). While each of these approaches has its own merit, they are all known to yield erroneous flow vector estimates under certain scenarios. Notably, Doppler/phase-shift estimation is prone to aliasing artifacts when tracking fast flow, whereas speckle tracking and directional cross-correlation have difficulty in following out-of-plane motion (Hansen L K, Udesen J, Oddershede N, Henze L, Thomsen C, Jensen J A, Nielsen M B. In vivo comparison of three ultrasound vector velocity techniques to MR phase contrast angiography. Ultrasonics, 2009; 49: 659-667; Swillens A, Segers P, Torp H, Lovstakken L. Two-dimensional blood velocity estimation with ultrasound: speckle tracking versus crossed-beam vector Doppler based on flow simulations in a carotid bifurcation model. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2010a; 57: 327-339). These frailties are particularly exposed when flow velocities vary significantly over different phases of a pulsatile flow cycle and when the imaging frame rate is inadequate (Swillens A, Segers P, Lovstakken L. Two-dimensional flow imaging in the carotid bifurcation using a combined speckle tracking and phase-shift estimator: a study based on ultrasound simulations and in vivo analysis. Ultrasound Med. Biol., 2010b; 36: 1722-1735).